Determine whether the BEST, most common interpretation of the given statement is:

     TRUE - Select 1

     FALSE - Select 2

Question 1 options

When the population standard deviation sigma is assumed known, a confidence interval can assume NORMALITY of the SAMPLE MEAN if the sample size is greater than 30.

INCREASING the confidence level of a confidence interval from 90% to 99% makes the interval SHORTER.

A CONFIDENCE INTERVAL can be interpreted as the single best ESTIMATE of a population parameter.

As the sample size INCREASES for computing a confidence interval, the width of the confidence interval DECREASES.

For a PROBABILITY DENSITY FUNCTION, the area between two values aand b is the probability a randomly selected individual will have a value between a and b.

A Z-SCORE can be interpreted for a value as the value's number of standard deviation above or below the mean.

A NORMAL distribution will have an approximately SYMMETRIC histogram.

As the STANDARD DEVIATION decreases for a normal distribution, the values become LESS concentrated around the MEAN.

The goal when using confidence intervals is to have WIDE INTERVALS to be assured that the interval contains the population parameter.

A SYMMETRIC histogram implies the plotted variable is NORMALLY distributed.

The probability that a patient recovers from a stomach disease is 0.6. Suppose 20 people are known to have contracted this disease. (Round your answers to three decimal places.)

(a)

What is the probability that exactly 14 recover?

(b)

What is the probability that at least 11 recover?

(c)

What is the probability that at least 14 but not more than 19 recover?

(d)

What is the probability that at most 16 recover?

You may need to use the appropriate appendix table or technology to answer this question.

Suppose 85% of the cars this plant produces are cherries. Both cherries and lemons can have Malfunctions in the first year of ownership. Suppose the probability that any car is both cherry and malfunction is .10. If a car is a lemon, the probability is .30 that it will malfunction in the first year.

A) What is the probability that any car is both a lemon and does not malfunction in the first year?

B) What is the probability that any car Malfunctions in the first year?

C) If a car malfunctions in the first year, what is the probability it is a lemon?

50. Which of the following correctly describes the meaning of the p-value?

A student answers a multiple choice examination with two questions that have four possible answers each. Suppose that the probability that the student knows the answer to a question is 0.80 and the probability that the student guesses is 0.20. If the student guesses, the probability of guessing the correct answer is 0.25. The questions are independent, that is, knowing the answer on one question is not influenced by the other question.

(a) What is the probability that the both questions will be answered correctly?

(b) If answered correctly, what is the probability that the student really knew the correct answer to both questions?

Consider a lottery game in which a person can win $0, $1, $2, or $1,000. The probability of winning nothing when one plays the game is 0.99, the probability of winning $1 is 0.009, and the probability of winning $2 is 0.0009.

1. If the game cost $1 to play what is the probability that a person will at least win their money back in the game?
2. What is the interval of values that are within one standard deviation of the mean?
3. What is the probability that the lottery winnings will be within one standard deviation of the mean?

From weather records, it is known that it is rainy in a particular city 35% of the time. When it is rainy, there is heavy traffic 80% of the time, and when it is not rainy, there is heavy traffic 25% of the time

. a. What is the probability that on a random day, it’s not raining and there is heavy traffic?

b. What is the probability that there is heavy traffic on a random day?

c. What is the probability that on a day with no rain there is no heavy traffic?

d. What is the probability that on a day with heavy traffic it is not raining?

e. What is the probability that if there is no heavy traffic, it is raining?

You would like to study the height of students at your university. Suppose the average for all university students is 67 inches with a SD of 18 inches, and that you take a sample of 19 students from your university.

a) What is the probability that the sample has a mean of 61 or less inches?
probability =  

b) What is the probability that the sample has a mean between 68 and 71 inches?
probability =  

Note: Do NOT input probability responses as percentages; e.g., do NOT input 0.9194 as 91.94.

Express the probability as a decimal with four digits after the decimal point. Show your work!

If one of the 1043 subjects is randomly selected, find the probability of selecting someone sentenced to prison.

Find the probability of being sentenced to prison, given that the subject entered a plea of guilty.

Find the probability of being sentenced to prison, given that the subject entered a plea of not guilty.

After comparing the results of questions b and c, what do you conclude of wisdom of entering a guilty plea?

If 1 of the subjects is randomly selected, find the probability of selecting someone who was sentenced to prison or entered a plea of guilty.

If 2 different subjects are randomly selected, find the probability that they both were sentenced to prison.

If 2 different subjects are randomly selected, find the probability that they both entered pleas of not guilty.

If 1 of the subjects is randomly selected, find the probability of selecting someone who entered a plea of not guilty or was not sentenced to prison.

If 1 of the subjects is randomly selected, find the probability of selecting someone who was sentenced to prison and entered a plea of guilty.

If 1 of the subjects is randomly selected, find the probability of selecting someone who was not sentenced to prison and did not entered a plea of guilty.